Equations
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Contents
1
Common DOE surfaces
1.1
Sinusoidal, triangle
1.2
Square, rectangle
1.3
Blazed, sawtooth
2
Holographic Deflectors (hologons)
Common DOE surfaces
Sinusoidal, triangle
Max D.E. ~ 30% +/-1 order
Power distribution follows Bessel function in the scaler region.
T
File:Simeq.gif
File:Lambda.gif
for transmission.
T
File:Simeq.gif
File:Lambda.gif
/ 4 for reflection.
Easily replicated or deep etch can yield higher efficiency.
Square, rectangle
Max D.E. ~ 40% +/-1 order.
Power distributions favors odd orders.
Pi phase shift typical.
Classic binary grating.
T
File:Simeq.gif
File:Lambda.gif
for transmission.
T
File:Simeq.gif
File:Lambda.gif
/ 4 for reflection.
Blazed, sawtooth
Max D.E ~ 98%
Reflection Case:
File:Lambda.gif
= 2 d sin a
T =
File:Lambda.gif
/ 2 +/- 10%
Transmission Case:
File:Lambda.gif
= d sin b
a
File:Simeq.gif
2b
T =
File:Lambda.gif
/ (n-1) +/- 10%
Surface shadows reduce D.E. by
File:Equ1.gif
Wavelength changes reduce D.E. by
File:Equ2.gif
Holographic Deflectors (hologons)
N =
File:Theta.gif
D / ( 1.4
File:Lambda.gif
)
N = number of resolvable spots
File:Theta.gif
= full scan angle in radians
D = beam diameter in microns
File:Lambda.gif
= wavelength
File:Phi.gif
= wedge angle of glass
Special case of linear scan and near wobble invariance
File:Invariance1.gif
max straight scan angle ~ 36 deg
Dynamic wobble
File:Dynwob1.gif
Wedge wobble = (n-1)
File:Phi.gif
Scan angle multiplier = 1.4 @ 90degrees cross scan angle
Last modified on 9/29/97
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